2(-2p^2+18p-9)=0

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Solution for 2(-2p^2+18p-9)=0 equation: 


Simplifying
2(-2p2 + 18p + -9) = 0

Reorder the terms:
2(-9 + 18p + -2p2) = 0
(-9 * 2 + 18p * 2 + -2p2 * 2) = 0
(-18 + 36p + -4p2) = 0

Solving
-18 + 36p + -4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 18p + -2p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 18p + -2p2)' equal to zero and attempt to solve:

Simplifying
-9 + 18p + -2p2 = 0

Solving
-9 + 18p + -2p2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
4.5 + -9p + p2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -9p + -4.5 + p2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -9p + p2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -9p + p2 = 0 + -4.5
-9p + p2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-9p + p2 = -4.5

The p term is -9p.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9p + 20.25 + p2 = -4.5 + 20.25

Reorder the terms:
20.25 + -9p + p2 = -4.5 + 20.25

Combine like terms: -4.5 + 20.25 = 15.75
20.25 + -9p + p2 = 15.75

Factor a perfect square on the left side:
(p + -4.5)(p + -4.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(p + -4.5) equal to 3.968626967 and -3.968626967.


Subproblem 1
p + -4.5 = 3.968626967

Simplifying
p + -4.5 = 3.968626967

Reorder the terms:
-4.5 + p = 3.968626967

Solving
-4.5 + p = 3.968626967

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '4.5' to each side of the equation.
-4.5 + 4.5 + p = 3.968626967 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + p = 3.968626967 + 4.5
p = 3.968626967 + 4.5

Combine like terms: 3.968626967 + 4.5 = 8.468626967
p = 8.468626967

Simplifying
p = 8.468626967


Subproblem 2
p + -4.5 = -3.968626967

Simplifying
p + -4.5 = -3.968626967

Reorder the terms:
-4.5 + p = -3.968626967

Solving
-4.5 + p = -3.968626967

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '4.5' to each side of the equation.
-4.5 + 4.5 + p = -3.968626967 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + p = -3.968626967 + 4.5
p = -3.968626967 + 4.5

Combine like terms: -3.968626967 + 4.5 = 0.531373033
p = 0.531373033

Simplifying
p = 0.531373033


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {8.468626967, 0.531373033}
Solution
p = {8.468626967, 0.531373033}

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